Understanding Derivatives

The video tutorial covers the basics of finding derivatives, starting with a review of derivative formulas, including the derivative of a constant, the derivative of x, and the power rule. It then provides examples of finding derivatives for various functions, such as constant functions, linear functions, and polynomial functions, while highlighting when to apply the power rule and when not to. The tutorial concludes with a practical example of finding the derivative of a polynomial function.

What is the derivative of a constant with respect to x?

• Zero

• Undefined

• The constant itself

• One

According to the power rule, what is the derivative of x^n with respect to x?

• x^(n-1)

• n * x^(n-1)

• x^n

• n * x^n

If f(x) = 5, what is f'(x)?

• x

• 1

• 5

• 0

For g(x) = 8x, what is g'(x)?

• x

• 1

• 0

• 8

Why don't we apply the power rule to f(x) = 2^3?

• Because 2^3 is a constant

• Because 2^3 is a variable

• Because 2^3 is a function

• Because 2^3 is an exponent

What is the derivative of g(x) = x^3?

• x^2

• x^3

• 3x^2

• 3x^3

For f(x) = π^7, what is f'(x)?

• 7π^6

• π^6

• π^7

• 0

What is the derivative of g(x) = 7x^9?

• 7x^8

• 63x^8

• 63x^9

• 9x^8

In the function g(x) = 7x^9, what role does the number 7 play?

• It is the derivative

• It is the base

• It is the exponent

• It is a constant multiplier

What is the result of applying the power rule to x^n?

• n * x^(n-1)

• x^n

• n * x^n

• x^(n-1)